Modern paper and paper board is predominantly composed of a matrix of wood fibres. During the consolidation stage of papermaking, individual wet fibres are drawn and entangled together forming a web structure. The deformability of the wet fibres used is a significant measure of the ability of the fibres to conform to each other by providing bonding contact in the course of dewatering, pressing, and drying. Fibre flexibility is a significant measure of fibre deformability. Fibres which are flexible are more conformable to one another, thus forming more contact area among fibres.
Fibre flexibility determines the total inter-fibre contact area and the voids in the fibre network, and plays a dominant role in determining most paper properties, such as bulk, permeability, opacity, surface smoothness, and physical strength.
The fibre flexibility of mechanical pulp, such as bleached chemi-thermomechanical pulp (BCTMP) fibres, is more important when BCTMP fibres are used in wood-free fine paper grades to improve paper bulk and opacity [1].
Compared with chemical pulp fibres, which usually collapse completely during fibre processing, mechanical pulp fibres do not collapse, or collapse only partially depending on the papermaking process [2]. Collapsed fibres have higher flexibility than uncollapsed fibres, so it is important to understand how fibre collapsibility affects the fibre flexibility.
Among all properties of wood fibres, the elastic modulus of the fibre is recognized as one of the most fundamental fibre properties that affects almost all paper qualities and papermaking properties, such as sheet density, physical strength, light scattering ability, smoothness, and permeability. It is the controlling factor that determines the deformability of the fibre wall.
There are several prior art methods for measuring the flexibility of individual wet fibres.
The measurement of single fibre elastic modulus is usually performed by micro-tensile testing. The difficulties associated with this test are the dimensions of individual wood fibres, which are short (1-5 mm) and thin (10-30 um in diameter) and require careful handling and mounting techniques in sample preparation, and accurate measurements for stress and strain in a very small scale. Because of the heterogeneous nature, a large population of fibres needs to be tested for the statistical analysis. Tedious and time-consuming operations in the fibre scale become a major drawback of this test method and make it impractical for engineering applications.
Some existing prior art methods treat the fibre as a cantilever [3-7]. Most of these methods are based on small deflection beam theory, which involves measuring the displacement of a fibre beam when applying a transverse force or bending moment on the fibre. If the fibre is treated as a beam subject to pure elastic deformation, the flexibility (F) of individual fibres can be defined as the reciprocal of its bending (also sometimes referred to as flexural stiffness) EI, where E is the elastic modulus of the fibre wall and I is the moment of inertia of the fibre cross-section: F=1/EI.
Seborg and Simmonds [8], for example, measured the stiffness of dry fibres by clamping individual fibres into place and then exerting a force on a fibre using a quartz spring to bend it like a cantilever beam. The flexural stiffness EI is determined from the slope of the load-deflection curve. The test suffers from two main disadvantages: (1) it is done on single fibres, making it very tedious and cumbersome; and (2) the clamping can damage the fibre.
James [9] calculated the fibre stiffness by measuring the resonance frequency of a fibre cantilever. Hydrodynamic or bending beam methods have also been developed for the fibre flexibility measurement by hydrodynamic forces generated by water flow and image analysis, so that individual fibre handling can be avoided.
Various methods have been developed for supporting the fibres. For example, Samuelsson [3] used a mechanical jaw to clamp fibres. Tam Doo and Kerekes [10] supported fibre on one end of a capillary tube so that mechanical damage to the fibre can be avoided. Like the Seborg and Simmonds method, the Tam Doo and Kerekes method is limited to testing individual fibres.
Kuhn et al. [6] developed a device that bends fibres by a T-junction tube when fibres in water flow out of a capillary. The fibre deformation is observed by a microscope and the force is calculated according to hydrodynamic theory. The Kuhn method is a direct measure of the flexibility of a fibre and may give flexibility results that are higher than expected [6].
Conformability testing as opposed to directly measuring flexibility is another typical method for fibre flexibility measurement. This method was first proposed by Mohlin [4]. In this method, a fibre is wet pressed onto a thin glass fibre (diameter=60 mm) that is fixed on a glass slide. The wet fibre arcs over the glass fibre and then is allowed to dry. The non-contact span, or freespan, length of the fibre is determined to calculate the fibre flexibility according to the beam deflection theory. Since only a conventional light microscope is required, and it can provide a numerical measure in an engineering unit, this method has commonly been used for fibre flexibility measurement [11-13]. No pressure, however, is applied to the fibre when taking the measurement and most likely does not approximate what happens in a paper structure of such fibres.
Steadman and Luner [7] have sought to improve upon the Mohlin method. In the Steadman method, the stiffness (flexibility) of individual wet fibres is determined from the elastic modulus (E) and the moment of inertia (I) of the fibre wall. This method is advantageous because it does not need to handle individual fibres. In the Steadman method, a wire of 25 μm diameter was used as the support wire for forming the fibre arc over it. A larger wire will lead to a larger arc, which will be easier to identify with a conventional microscope, but a large wire will also increase the deflection ratio.
In the Steadman method, fibres are wetted and pressed onto a thin support wire that is fixed on a glass slide. The fibre and the support wire are approximately 90 degrees to one another such that when pressed onto the wire, the fibre forms an arch-like span over the wire as it deforms. The fibre is then allowed to dry and the sections of the fibre in contact with the slide become adhered to the glass slide. The length of the section of the span not in contact with the glass slide, referred to as the non-contact span or freespan length, is measured from above using a conventional light microscope with incident lights, under which the optical contact zone of the fibre and the glass slide appears in dark, whereas the non-contact zone appears in light, thus the freespan length is measured. The freespan length measurement is then used in the calculation of flexibility according to the following formula:F=1/EI=72d/PWS4 Where E=modulus of elasticity (Nm−2)                I=moment of inertia (m4)        d=wire diameter (m)        P=pressing pressure (Nm−2)        W=projected fibre width (m)        S=mathematical estimate of the loaded span (m)        
The fibre at which the distance between fibre surface and the glass slide is less than half of the wavelength of the light (usually assumed as 550 nm) appears in dark even if they are not contacted physically due to light interference; therefore, the freespan length is usually under-measured. Since the fibre thickness is not uniform and a fibre does not collapse uniformly along the fibre length, the thickness of the fibre cross-section affects the freespan length used for the stiffness calculation, which is neglected in this method as the conventional light microscope only generates images from the top view.
Since the moment of inertia of a fibre cross-section cannot be measured using a conventional light microscope (LM), the Steadman method has only been used for measuring fibre flexibility but not for measuring the elastic modulus. The elastic modulus can be solved only if the moment of inertia of the fibre is known but prior art methods do not yield the moment of inertia.
As discussed above, in the Steadman method, a LM is employed to observe pulp fibres. In recent years, confocal laser scanning microscopes (CLSM) have been used in pulp and paper research as an alternative to LMs for imaging fibres. However, CLSMs have not been used to take optical sections of fibres. Even where CLSMs have been used to image fibre cross-sections, the images have been of the cross-sectional surfaces of fibres which have been physically cut into cross-sections.